Friday, September 22, 2017

Before the arrival of hurricane Irma in Florida, the Pasco county sheriff's department posted a tweet that quickly went viral, urging citizens not to try and scare off the hurricane:

Thanks, Sheriff.

This didn't come out of nowhere—the tweet was a response to an article about a (tongue-in-cheek) facebook event encouraging people to shoot at the hurricane, which attracted about 40,000 "interested" fans. Hopefully, nobody took it too seriously and actually went out to take a stand against Irma with their shotguns.

But, being the kind of people we are, this sparked a discussion at the office. You know the kind; "Okay, we shouldn't shoot at the hurricane...*long pause*...but what if we DID?" Could you stop a hurricane by shooting at it? Kinetic energy is kinetic energy, whether it's in a gust of wind or an onrushing attacker—so why couldn't the "stopping power" of a .44 magnum (or a few million of them) stop a force of nature? Let's say you're at the edge of the hurricane, and fire a bullet against the wind into the approaching side of the storm. If the round doesn't come out the other side of the storm before it loses all its momentum, that means that all the kinetic energy of the bullet has been transferred to the air mass. If they're heading in opposite directions, every bullet fired ought to reduce the intensity of the hurricane by a small amount.

This highly scientific diagram should help.

So, having gotten it out of the way that you ABSOLUTELY SHOULD NOT DO THIS, how many bullets would it have taken to kill Irma dead?

To find out, the first thing we'd need to know how much kinetic energy was in the storm. Fortunately, this data is pretty easy to find—most weather scientists regard the integrated kinetic energy (or IKE) of a hurricane as an important tool to assess the intensity of the storm—and its potential for damage. Many even prefer it to the more familiar Saffir-Simpson scale; when you hear a storm described as "Category 4" or "Cat. 5", this is the Saffir-Simpson categorization, which relies on top sustained wind speeds. But a big, spread-out storm with lower top wind speeds could do more damage than a tightly bound hurricane with higher velocities, so some argue that it's best to look at the IKE.

The neat thing is that the kinetic energy of a moving air mass is calculated in much the same way as the kinetic energy in something familiar like a car—it's simply half the mass times the square of its velocity. We know how much mass is in a cubic meter of air, and weather instruments in the path of a storm tell us how fast that air is moving at certain points, so by treating each cubic meter of air as a massive object moving at the measured windspeed, we can calculate the storm's IKE!

That's clearly a colossal amount of energy. But consider this: if you summed up all the energy that the world used in 2014—all the fossil fuels burnt, the solar power collected, the nuclear energy generated, etc.—you've got 570 exajoules—4.5 million timesthe amount of energy in hurricane Irma. Being so small as individuals, it's easy to feel dwarfed by the forces of nature; it's easy to forget that, together, we're more powerful than a hurricane...by orders of magnitude.

As awe-inspiring as that is, it's also a sobering reminder that, if we're not careful about how we use that energy, we can wreak some serious havoc on our environment: with great power comes great responsibility, and 570 exajoules per year is a LOT of power.

But for right now, let's forget responsibility (this is just a thought experiment, after all)—and in true American fashion...let's lock 'n load. We've determined that, at least in theory, we've got power at the scale it would take to stop a hurricane. But how many bullets would it take?

We know the IKE of a storm like Irma, so once we find the kinetic energy of a bullet, figuring this out is a matter of simple division. But the kinetic energy of a bullet varies an awful lot depending on the kind of ammunition we're talking about: remember that the kinetic energy that propels a round comes from prepackaged chemical energy—the explosive powder that's in the bullet casing.

That means the number of bullets we'll need depends way more on the type of ammo than our choice of firearm, but we already know that we're going to need a lot of firepower here. So let's go with something fast-firing and high-impact.

Hmm...this should do nicely.

That would be the General Electric M134 minigun, capable of firing 6,000 rounds per minute at a muzzle velocity of 850 m/s. The kinetic energy of a Each bullet, according to the wiki specifications for the 7.62x51mm NATO ammunition that it uses, carries roughly 3,300 J of energy. In terms of kinetic energy transfer, this monster is pretty much unparalleled until you get into things like heavy ordnance, or absurd and unsustainable designs like the "million rounds per minute" Metal Storm.

Operating at maximum capacity, the M134 is capable of spitting out nearly 20 million joules of energy per minute. That's a pretty extraordinary amount, but it's still many orders of magnitude shy of the amount of energy in a hurricane like Irma—a Terajoule is a trillion joules, i.e. a million million.

So how many bullets are we going to need? If there's 125 trillion joules in the storm, and 3300 in a bullet, we'd need 125 TJ/3300 J = 3.79*1010 rounds to completely undo Irma. 109 is a billion, so that means 37.9 billion rounds. A quick search around the web tells us that 10-12 billion is a good guess for the number of bullets manufactured annually, so we'd need a truly alarming ammo stockpile to begin with.

But how much firepower are we going to need here? Let's say we've convinced the Commander in Chief that this is an issue of national security, and we've got the resources of the entire DoD at our disposal—all the manpower and miniguns we need—but we've only got 24 hours to disperse the storm.

To fire off the necessary 37.9B rounds from a single minigun operating continuously at 6,000 rounds per minute would take 4387 days, or twelve years. That's not going to do us much good for stopping the storm—but it means that, if we want to get it done in 24 hours, all we need is 4387 miniguns!

Obviously, there are logistical problems here—guns overheat and need to be cooled, need reloading, jam up, etc. If you spray enough lead into the approaching edge of a hurricane, some of it IS going to start coming back at you before the storm disperses, and could return at velocities of up to 70 m/s—like being shot at with an old-school black powder musket. On the other hand, you probably don't need to counter ALL the energy in the hurricane to downgrade it to a non-destructive tropical storm, so let's just assume (in the true spirit of Fermi Problem Friday) that those factors balance out.

So there you have it, folks: if you wanna kill a hurricane with bullets, all you need is 24 hours, a fortified brigade of heavy artillerymen, and $20 billion worth of ammunition. Of course, in the process, you'd probably put enough lead in the water to poison the entire eastern seaboard...so maybe don't expect a medal.